Finite Group Databasebeta

← #524658

Subgroups — #524658

Order 512.

3946 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2C2×#2352C211yesmaximal, characteristic
3C2×#2293C211yesmaximal, characteristic
4#14709C211yesmaximal, characteristic, complemented
5#14505C214yesmaximal
6#14451C214yesmaximal, complemented
7#14258C211yesmaximal, characteristic, complemented
8#14258C211yesmaximal, characteristic, complemented
9#14160C211yesmaximal, characteristic, complemented
10#14139C211yesmaximal, characteristic, complemented
11#14138C211yesmaximal, characteristic, complemented
12#14102C214yesmaximal, complemented
13#13943C214yesmaximal, complemented
14#13942C211yesmaximal, characteristic, complemented
15#13939C211yesmaximal, characteristic, complemented
16#13924C211yesmaximal, characteristic, complemented
17#13795C211yesmaximal, characteristic, complemented
18#13795C211yesmaximal, characteristic, complemented
19C4×#391C211yesmaximal, characteristic, complemented
20C2×#552—28no—
21C2×#552—28no—
22C2×#552C4116yescomplemented
23C22×#126C2212yes—
24C22×#125C2211yescharacteristic
25C22×#125C2212yes—
26C22×#123C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C22×#117C2212yes—
36C23×C4⋊C4C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38#2352—28no—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43#2293—28no—
44C2×#390C2212yes—
45C2×#389C2212yes—
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#387C2212yes—
50C2×#386C2212yes—
51C2×#382C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C43C2211yescharacteristic
60#1445C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1436C2214yes—
71#1436C2214yes—
72#1436C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75C4⋊#95C2214yes—
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89#1434C2214yes—
90#1434C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C4×#95C2214yes—
96C23×Q8C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2312yes—
102#552—2128no—
103C2×#126—28no—
104C2×#126—28no—
105C2×#126C2×C4116yes—
106C2×#125—28no—
107C2×#125—28no—
108C2×#125—24no—
109C2×#125—24no—
110C2×#125C2×C4116yescomplemented
111C2×#125C2×C418yescomplemented
112C2×#123—28no—
113C2×#123—28no—
114C2×#123C2×C4116yes—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8C2×C418yes—
120C2×C22⋊Q8C2×C418yescomplemented
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8C2×C418yescomplemented
124C2×C4×D4C2×C418yes—
125C2×C4×D4D418yes—
126C2×C4×D4D418yes—
127C2×#117—24no—
128C2×#117—24no—
129C2×#117—24no—
130C2×#117—24no—
131C2×#117—24no—
132C2×#117—24no—
133C2×#117—28no—
134C2×#117—28no—
135C2×#117—24no—
136C2×#117—24no—
137C2×#117—42no—
138C2×#117—42no—
139C2×#117—42no—
140C2×#117C2×C418yes—
141C2×#117C2×C4116yescomplemented
142C22×C4⋊C4—24no—
143C22×C4⋊C4—24no—
144C22×C4⋊C4—24no—
145C22×C4⋊C4—24no—
146C22×C4⋊C4—42no—
147C22×C4⋊C4C2×C418yescomplemented
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2311yescharacteristic
181C22×C42C2312yes—
182C22×C42C2312yes—
183C22×C42C2312yes—
184C22×C42C2312yes—
185C22×C42C2311yescharacteristic
186C22×C42C2312yes—
187C22×C42C2312yes—
188C22×C42C2311yescharacteristic
189#391—24no—
190#391—24no—
191#391—42no—
192#391—42no—
193#390—28no—
194#389—28no—
195#388—28no—
196#388—28no—
197#388—28no—
198#387—28no—
199#386—28no—
200#382—24no—
201#380—24no—
202#380—24no—
203C4×C4⋊C4—24no—
204C4×C4⋊C4—24no—
205C4×C22⋊C4—24no—
206C4×C22⋊C4—24no—
207C4×C22⋊C4—28no—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C43—24no—
233C25C2411yescharacteristic
234C25C2411yescharacteristic
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8C22×C414yes—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4C22×C414yes—
245C22×D4C2×D414yes—
246C22×D4C2×D414yes—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4—42no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4C22×C414yes—
265C23×C4C22×C414yes—
266C23×C4C22×C418yes—
267C23×C4C2×D414yes—
268C23×C4C2×D414yes—
269C23×C4C2×D414yes—
270C23×C4C2×D414yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288#126—264no—
289#125—264no—
290#125—232no—
291#123—264no—
292C22⋊Q8—232no—
293C22⋊Q8—232no—
294C4×Q8—232no—
295C4×D4C22⋊C4164yes—
296#117—232no—
297#117—264no—
298#117—416no—
299#117—416no—
300#117—416no—
301C2×C4⋊C4—232no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—416no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4C22×C414yes—
345C2×C4⋊C4C22×C414yes—
346C2×C4⋊C4C22×C418yes—
347C2×C4⋊C4C22×C414yes—
348C2×C4⋊C4C22×C418yes—
349C2×C4⋊C4C22×C418yes—
350C2×C4⋊C4C22×C418yes—
351C2×C4⋊C4C22×C418yes—
352C2×C4⋊C4C22×C418yes—
353C2×C4⋊C4C22×C414yes—
354C2×C4⋊C4C2×D414yes—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4#4114yes—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4C22×C418yes—
383C2×C22⋊C4C22×C418yes—
384C2×C22⋊C4C22×C418yes—
385C2×C22⋊C4C22×C414yes—
386C2×C22⋊C4C22×C414yes—
387C2×C22⋊C4C2×D414yes—
388C2×C22⋊C4C2×D414yes—
389C2×C22⋊C4C2×D414yes—
390C2×C22⋊C4C2×D414yes—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—42no—
416C2×C42—44no—
417C2×C42C22×C418yes—
418C2×C42C22×C418yes—
419C2×C42C22×C414yes—
420C2×C42C2×D414yes—
421C2×C42C2×D414yes—
422C2×C42#4114yes—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—28no—
432#95—28no—
433#95—28no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95—44no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—21no—
456C24—21no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24C23×C412yes—
464C24C23×C412yes—
465C24C22×D412yes—
466C24C22×D412yes—
467C24C22×D412yes—
468C24C22×D412yes—
469C24C2511yescharacteristic
470C2×Q8—28no—
471C2×Q8—28no—
472C2×Q8—28no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4C2×C22⋊C4116yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—216no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—416no—
571C22×C4—48no—
572C22×C4—416no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—88no—
577C22×C4—84no—
578C22×C4—88no—
579C22×C4C2×C22⋊C4116yes—
580C22×C4C2×C22⋊C4116yes—
581C22×C4C23×C414yes—
582C22×C4C23×C414yes—
583C22×C4C23×C414yes—
584C22×C4C23×C414yes—
585C22×C4C23×C412yes—
586C22×C4C23×C412yes—
587C22×C4C23×C412yes—
588C22×C4C23×C412yes—
589C22×C4C23×C412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C2×#4114yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C42−1+414yes—
606C22×C42−1+412yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—216no—
610C4⋊C4—28no—
611C4⋊C4—216no—
612C4⋊C4—216no—
613C4⋊C4—216no—
614C4⋊C4—216no—
615C4⋊C4—216no—
616C4⋊C4—28no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4C2×C22⋊C4116yes—
625C22⋊C4—216no—
626C22⋊C4—216no—
627C22⋊C4—216no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4C2×C22⋊C4116yes—
636C22⋊C4C2×C22⋊C4116yes—
637C42—216no—
638C42—216no—
639C42—28no—
640C42—48no—
641C42—48no—
642C42—48no—
643C42—44no—
644C42—44no—
645C42—44no—
646C42—84no—
647C42C2×C22⋊C4116yes—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23C22×C22⋊C414yes—
693C23C22×C22⋊C414yes—
694C23C24×C411yescharacteristic
695C23C23×D411yescharacteristic
696C23C23×D411yescharacteristic
697C23C22×#4111yescharacteristic
698C23C22×#4111yescharacteristic
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×2−1+411yescharacteristic
701C23C2×2−1+412yes—
702C23#58512yes—
703C23#58512yes—
704C23#58512yes—
705Q8—416no—
706D4—416no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—232no—
728C2×C4—232no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—432no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—816no—
801C2×C4C22×C22⋊C414yes—
802C2×C4C22×C22⋊C414yes—
803C2×C4C22×C22⋊C414yes—
804C2×C4C22×C22⋊C414yes—
805C2×C4C22×C22⋊C414yes—
806C2×C4C4×#4114yes—
807C2×C4#52014yes—
808C2×C4#54614yes—
809C2×C4#54614yes—
810C2×C4#54714yes—
811C2×C4#54714yes—
812C22—24no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—44no—
827C22—44no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—44no—
833C22—44no—
834C22C23×C22⋊C411yescharacteristic
835C22C2×C4×#4111yescharacteristic
836C22C2×#52011yescharacteristic
837C22#342812yes—
838C22C4×2−1+412yes—
839C22#344912yes—
840C22#344911yescharacteristic
841C22#344911yescharacteristic
842C22C2×#54611yescharacteristic
843C22C2×#54611yescharacteristic
844C22C2×#54711yescharacteristic
845C22C2×#54711yescharacteristic
846C22#348912yes—
847C22#349911yescharacteristic
848C22#350011yescharacteristic
849C22#350712yes—
850C22#351212yes—
851C22#351612yes—
852C22#352112yes—
853C22#354712yes—
854C22#355112yes—
855C22#356312yes—
856C22#356512yes—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—24no—
861C4—44no—
862C4—44no—
863C4—44no—
864C4—44no—
865C4—44no—
866C4—44no—
867C4—44no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4#233918yes—
874C2—44no—
875C2—44no—
876C2#3404411yescharacteristic
877C2C2×#233911yescharacteristic
878C2#3425911yescharacteristic
879C2#3431812yes—
880C2#3448212yes—
881C2#3891512yes—
882C2#3894611yescharacteristic
883C2#3894711yescharacteristic
884C2#3946312yes—
885C2#3948411yescharacteristic
886C2#3948511yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #14709C2semidirect
6. #14451C2semidirect
7. #14258C2semidirect
8. #14258C2semidirect
9. #14160C2semidirect
10. #14139C2semidirect
11. #14138C2semidirect
12. #14102C2semidirect
13. #13943C2semidirect
14. #13942C2semidirect
15. #13939C2semidirect
16. #13924C2semidirect
17. #13795C2semidirect
18. #13795C2semidirect
19. C4×#391C2semidirect
22. C2×#552C4semidirect
110. C2×#125C2×C4semidirect
111. C2×#125C2×C4semidirect
120. C2×C22⋊Q8C2×C4semidirect
123. C2×C4×Q8C2×C4semidirect
141. C2×#117C2×C4semidirect
147. C22×C4⋊C4C2×C4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#5522
C2×#23522
C2×#22932
#147092
#145052
#144512
#142582
#141602
#141392
#141382
#141022
#139432
#139422
#139392
#139242
#137952
C4×#3912